Problem Set A (1) The following is known about three numbers: Three times the first number plus the second number plus twice the third number is 5. If 3 times the second number is subtracted from the sum of the first number and 3 times the third number, the result is 2. If the third number is subtracted from 2 times the first number and 3 times the second number, the result is 1. (a) Write a system of equations to match the description of the information given. (b) Find the numbers using Cramer's Rule.
Problem Set A (1) The following is known about three numbers: Three times the first number plus the second number plus twice the third number is 5. If 3 times the second number is subtracted from the sum of the first number and 3 times the third number, the result is 2. If the third number is subtracted from 2 times the first number and 3 times the second number, the result is 1. (a) Write a system of equations to match the description of the information given. (b) Find the numbers using Cramer's Rule.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Problem Set A
(1) The following is known about three numbers: Three times the first number plus the second
number plus twice the third number is 5. If 3 times the second number is subtracted from
the sum of the first number and 3 times the third number, the result is 2. If the third number
is subtracted from 2 times the first number and 3 times the second number, the result is 1.
(a) Write a system of equations to match the description of the information given.
(b) Find the numbers using Cramer's Rule.
(2) A certain brand of tea bags comes in packages of 5, 10, and 20 sachets, costing
$5, $9, and $15 per package, respectively.
A store sold 16 packages containing a total of 165 sachets and took in $140.
(a) Write a system of equations to match the description of the information given.
(b) Determine how many packages of each type were sold using the Inverse Method.
(3) A company manufacturing laundry sinks has fixed costs of $100 per day but has total
costs of $2,500 per day when producing 15 sinks. The company has a daily demand function
of q = 360 – p, where q is the number if laundry sinks demanded and p is te price of
a laundry sink.
(a) If we assume that the total cost per day is linearly related to the amount of sinks
produced in a day, derive the total cost function of the company?
(b) Find a function for the average cost of this company.
(c) If production increases continuously, what is likely to be the average cost per sink?
(d) How many laundry sinks will the company need to produce in order to maximise it's profits?
(e) What is the maximum profit?
Problem Set B
1. The demand function for a good is given by the equation P
cost function is TC = dQ² + eQ + f, where a, b, d, e and f are positive constants.
(a) Derive the equation for profit.
(b) Derive an expression for the value of Q for which profit is maximised.
(2) For the f(x) = -x³ + 3x + 6 determine the coordinates of the turning point(s) and
any point(s) of inflection, if they exist.
= a -
- bQ while the total
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